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Answer:
x + 3 +
Step-by-step explanation:
Divide using Synthetic division
dividing by ( x - 3)
Using 0 to represent the x- term
3 | 1 0 4
↓ 3 9
+ +
------------------
1 3 13 ← remainder
Thus
= x + 3 +
Rationalize both the numerator and denominator. Given
we can rationalize it by introducing conjugates of the numerator and denominator:
Then the limit is equivalent to
For the remaining expression, divide through uniformly by :
As <em>n</em> goes to infinity, the remaining terms containing <em>n</em> converge to 0, leaving
making the overall limit 3.